**2.3 Hybrid model of the battery-pack**

As a result of these combined time- and frequency-domain tests, an electrical circuit has been determined. Also, the model includes an integration current SOC estimator, to guarantee that the parameters of the electrical circuit simulate the dynamic behavior of the battery-pack for different SOC conditions, as shown in **Figure 7**. The inputs of the model are the initial value of SOC (*SOC0*), the batterypack capacity (*Cn*), and the current (*ipack*). The output corresponds to the voltage response of the battery-pack (*upack*), which is calculated by Eq. (2), where *uRo*, *uc1*,

#### *Research Trends and Challenges in Smart Grids*


#### **Table 3.**

*Battery-pack impedance parameters.*

**Figure 7.** *Battery-pack model.*

*uc2*, and *uc3* simulate the voltage response of the ohmic resistance and each *RC* network, respectively:

$$\begin{aligned} \boldsymbol{\mu}\_{\text{puck}}\text{(SOC,t)} &= \boldsymbol{Eo}\text{(SOC,t)} - \boldsymbol{\mu}\_{\text{Ro}}\text{(SOC,t)}\\ &- \boldsymbol{\mu}\_{\text{C1}}\text{(SOC,t)} - \boldsymbol{\mu}\_{\text{C2}}\text{(SOC,t)} - \boldsymbol{\mu}\_{\text{C3}}\text{(SOC,t)}\text{ (2)} \end{aligned}$$

where:

$$
\mu\_{Ro}(\text{SOC}, t) = R\_o(\text{SOC}) \cdot ipack(t) \tag{3}
$$

$$
\mu\_{Ro}(SOC, t) = R\_o(SOC) \cdot ipack(t) \tag{3}
$$

$$
\mu\_{C1}(SOC, t) = \int\_{\overline{C\_1(SOC)}} \cdot \left( ipack(t) - \frac{u\_{C1}(SOC)}{R\_1(SOC)} \right) \cdot dt \tag{4}
$$

$$
\mu\_{C2}(SOC, t) = \int\_{\overline{C\_2(SOC)}} \cdot \left( ipack(t) - \frac{u\_{C2}(SOC)}{R\_2(SOC)} \right) \cdot dt \tag{5}
$$

$$
\mu\_{C2}\text{(SOC,t)} = \int\_{C\_2\text{(SOC)}} \frac{1}{C\_2\text{(SOC)}} \cdot \left( ipack\left(t\right) - \frac{\mu\_{C2}\text{(SOC)}}{R\_2\text{(SOC)}} \right) \cdot dt \tag{5}
$$

$$
\mu\_{C3}\text{(SOC,t)} = \int\_{C\_3\text{(SOC)}} \frac{1}{C\_3\text{(SOC)}} \cdot \left( ipack\left(t\right) - \frac{\mu\_{C3}\text{(SOC)}}{R\_3\text{(SOC)}} \right) \cdot dt \tag{6}
$$

$$u\_{C3} \text{(SOC,t)} = \int\_{C\_3(SOC)} 1 \cdot \left( ipack \left( t \right) - \frac{u\_{C3}(SOC)}{R\_3(SOC)} \right) \cdot dt \tag{6}$$

**151**

**Figure 9.** *Test bench picture.*

**Figure 8.**

*HIL simulation control setup.*

*Hybrid Modeling Procedure of Li-Ion Battery Modules for Reproducing Wide Frequency…*

data acquisition systems (in the case of electric applications). To perform the HIL simulation of the battery-pack, the experimental setup shown in [26] is used. In this test bench, the load regime is simulated by means of a MATLAB/Simulink model (software simulation). This current signal is used to control (by DSpace control system) the output signal of an electronic load and a power source connected in parallel to reproduce the charging/discharging cycles. This configuration is called hardware simulation; in this way, real devices are used to test the battery-pack. A control schema of the HIL simulation is shown in **Figures 8** and **9** that presents a

Three simulations of the battery-pack performance under dynamic regimes associated with distribution grids operation have been analyzed. The first one corresponds to a load frequency control application (LFC), which is related to grid frequency control, with typical time constants ranging from 0.2 ms to 10 s. The second one reproduces the dynamic voltage support (DVS) of a renewable energy source during 110 s. The simulated models of these load regimes are based on the operation of a hybrid ac/dc microgrid presented in [29]. Finally, the third one simulates the performance of an energy support device uninterruptible power supply (UPS). The time duration of this energy support is less than 30 min; and to

*DOI: http://dx.doi.org/10.5772/intechopen.88718*

picture of the test bench.
